ESTIMATION AND VALID ATION OF URBAN VEGETATION ABUNDANCE BY
SPECTRAL MIXTURE ANA LYSIS
Christopher Small 1 and Jacqueline Lu
1Lamont
Doherty Earth Obs.
Columbia University
Palisades NY, 10964 USA
small@LDEO.columbia.edu
2City
of New York/ Parks & Recreation
Olmsted Center -Flushing Meadow Corona Park
Flushing, NY 11368 USA
Jacqueline.Lu@parks.nyc.gov
KEY WORDS: urban, vegetation, Quickbird, Landsat
ABSTRACT:
Moderate resolution (< 50 m) optical sensors can provide multitemporal imagery of urban
vegetation distribution and abundance. Given a rigorous, repeatable and verifiable method for
estimating vegetation abundance, this imagery could provide important inputs to mesoscale models
of ecologic, hydrologic, climatic processes. Spectral mixture analyses produce vegetation fraction
estimates that can be radiometrically rectified for change analyses and can be validated with high
spatial resolution (<5 m) optical imagery. A simple three endmember linear mixture mode l
produces stable estimates of vegetation fraction for a wide range of land use types in New York
City. These estimates agree to within 10% with aggregated 2.8 m estimates derived from Quickbird
imagery. The observed scatter between the 30 m Landsat estimates and the aggregated 2.8 m
Quickbird estimates is generally less than 10% and cannot be explained by estimation error alone.
The form of the scatter can be explained by a combination of estimation error and subpixel spatial
uncertainty in the registration of the Landsat imagery. The scatter is consistent with a 6%
estimation error combined with a 17 m spatial misregistration between the Landsat and Quickbird
imagery
INTRODUCTION
Vegetation abundance and distribution are primary determinants of urban environmental
conditions. In addition to its obvious aesthetic importance, vegetation exerts a strong influence on
mass and energy fluxes through the urban environment by modulating evapotranspiration and
absorption of solar radiation. Accurate mapping and monitoring of vegetation distribution and
condition is central to the understanding of urban ecosystems. Urbanization is a dominant
demographic trend and the resultant land use and land cover change has been identified as one of
the three major global impacts of humans {Vitousek, 1994}. The growing presence and importance
of cities makes these human-dominated ecosystems ideal laboratories for the study of ecological
change. Resource managers also use information on the abundance, condition and spatial
distribution of urban vegetation for park and natural area management and urban planning. While in
situ data collection is the primary means of monitoring urban vegetation, remotely sensed
observations can provide valuable complements to traditional field observations.
New York City, most famous for its skyscrapers and worldly population, is also home to an
estimated 5.2 million trees {Nowak, 2002}. New York City’s vegetation is comprised of a
patchwork of remnant forests, inherited estates, neighborhood parks and playgrounds, green
streetscapes, parkways and private backyards and roof gardens. New York City Parks & Recreation
has jurisdiction for over half of the estimated 5 million total trees in the city. In 1996, Parks &
Recreation mobilized over 700 volunteers to conduct a comprehensive census of all the street trees
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in New York City. The census counted over 498,000 street trees in New York City, comprising of
approximately 70 different varieties. The vast majority of trees, however, comprise a small number
of species; over 40% of the street tree population consists of just two species. New York City’s
street trees are relatively small, with almost 60% measuring less than 12 inches diameter at breast
height {Watt, 1998}. However, many other types of vegetation in New York City, managed or
impacted by Parks and at least another dozen city, state, and federal agencies and private actors, are
not well characterized through on the ground inventories. Management of New York’s trees by the
Parks Dept. relies on the street tree census to represent the spatial distribution and health of its
vegetative assets.
Quantitative estimates of vegetation abundance derived from moderate and high spatial resolution
optical sensors have the potential to be used for operational monitoring of urban vegetation.
Operational use of these data requires a robust methodology for converting measurements of optical
radiance to accurate and verifiable estimates of vegetation abundance. A primary requirement for
operational use of remotely sensed vegetation abundance estimates is that they provide physical
units that can be compared directly with other measures of vegetation abundance and condition.
Spectral Mixture Analysis (SMA) satisfies this requirement by providing pixel-scale estimates of
areal abundance of spectral endmembers. In recent years SMA has been used for a variety of urban
land cover mapping applications (e.g. [Kressler and Steinnocher, 1996] [Small , 2001] [Rashed et
al., 2002] [Wu and Murray, 2003] {Weng, 2004}). In comparison to vegetation indices (e.g.
Normalized Difference Vegetation Index (NDVI)), SMA offers the advantage of providing
estimates of areal vegetation abundance that can be compared directly to other measures of
vegetation cover per unit area. In spite of its increasingly widespread use, most spectral mixture
analyses do not validate the endmember fraction estimates they produce. [Elmore et al., 2000]
devised a thorough field validation methodology based on point frame transect measurement of
individual plants in a semi-arid environment but the procedure is very labor intensive and not
suitable for environments containing large trees. [Small, 2001] proposed a methodology for high
spatial resolution vegetation abundance measurement from aerial photographs but the procedure
relies on manual selection of specific validation sites also somewhat labor intensive. In light of the
current availability of calibrated moderate (< 30 m) and high (< 5 m) resolution multispectral
imagery from Landsat ETM+, Ikonos and Quickbird, the potential for quantitative validation of
fractional abundance estimates has increased considerably since the time these earlier studies were
conducted. High spatial resolution imagery also provide a means to examine the structural
characteristics of moderate resolution (~20-40 m) targets as well.
The objectives of this study are to define operational procedures for moderate resolution vegetation
fraction estimation and validation and to examine some of the factors that limit the use of vegetation
fraction estimates for urban applications. In the first part of the analysis we summarize the
procedure used to derive vegetation fraction estimates from Landsat and Quickbird imagery. This
procedure is explained in greater detail in [Small, 2001] and {Small, 2003}. In the second part of
the analysis we quantify the agreement between the moderate and high resolution estimates and
investigate the effects of estimate error and spatial misregistration. The discussion focuses on the
physical interpretation of vegetation fraction estimates and comparison to in situ measures of urban
vegetation abundance.
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DATA
Both images used in this study were acquired in August 2002. At the time, the New York metro
area was experiencing draught conditions following several years of below average rainfall.
Although some smaller trees were experiencing premature senescence by August, the vegetation
abundance within the study area was equivalent to full leaf-on conditions at the time that both
images were acquired. We do not expect that the vegetation cover changed significantly between
the times the images were acquired. The Landsat ETM+ image (p.14, r.32) used in this study was
acquired on 14 August 2002 at 9:45 AM local time. Image Dns were converted to exoatmospheric
reflectance units as described by Markham and Barker (1986, 1987) and in the Landsat 7 Users
Handbook (http://ltpwww.gsfc.nasa.gov/IAS/handbook/handbook_toc.html). No atmospheric
correction was applied. The Quickbird imagery was acquired 2 August 2002 at 10:48 AM from a
viewing angle of 68°. Image DNs were converted to at-sensor radiance using parameters provided
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by Digital Globe. Spatial accuracy of the georegistered image was verified to be within 31 meters
by comparison with 48 validation sites derived from a Garmin 12 Map handheld GPS receiver.
SPECTRAL MIXTURE ANA LYSIS
Spectral Mixture Analysis (SMA) is a methodology whereby an observed radiance is modeled as a
linear mixture of spectrally pure endmember radiances. Linear mixture models are based on the
observation that, in many situations, radiances from surfaces with different "endmember"
reflectances mix linearly in proportion to area within the IFOV ([Johnson et al., 1983; Singer, 1981;
Singer and McCord , 1979]). This observation has made possible the development of a systematic
methodology for spectral mixture analysis ([Adams et al., 1993; Adams et al., 1986; Gillespie et al.,
1990; Sabol et al., 1992; Smith et al., 1990]) in which land surface reflectance variations are
represented by a set of endmember fraction images describing spatial variations in the areal
abundance of each endmember.
Endmember fractions were estimated with a constrained least squares inversion following the
procedure described in detail by [Small, 2001]. The resulting fraction and RMS error distributions
– shown in Figure 1 - are very similar to those obtained by Small (2001). This is to be expected
given the similarity in the study area and endmember spectra. As in the previous study, the largest
misfits are associated with areas of exposed soil and isolated high albedo targets. This is consistent
with the lack of a soil endmember in the model and the fact that the mixing space diverges near the
High Albedo endmember. RMS error diminishes with increasing fractions of Dark and Vegetation
endmembers. This indicates that the inverse problem is well posed with respect to vegetation
fraction estimation. RMS error is generally less than 0.02 reflectance units, suggesting that the 3
endmember linear model is capable of replicating the observed mixed reflectances quite closely.
This does not, however, guarantee that the fraction estimates are accurate. The accuracy must be
determined through validation.
VALIDATION
We validate the ETM+ vegetation fraction estimates by quantifying their degree of correspondence
to vegetation fraction estimates derived from Quickbird multispectral imagery. The 2.6 meter
spatial resolution of the Quickbird sensor allows it to image the individual components of the urban
mosaic at significantly higher spatial resolution than the 20 to 30 meter characteristic scale
estimated for the New York urban mosaic (Small, 2003). This is why individual features like
buildings, sidewalks, streets and trees can be identified in Quickbird imagery. The 2.6 meter
resolution is more than adequate to image medium to large tree crowns and to detect the presence of
fairly small street trees. At the 30 meter scale of the ETM+ IFOV, each 2.6 meter Quickbird pixel
represents less than 1% of the area within the Full Width Half Max of the ETM+ point spread
function.
This is more than adequate to represent the spatial scale of the dominant targets
responsible for the multiple scattering that is the primary source of nonlinear mixing within the
ETM+ IFOV. Because nonlinear mixing is the primary source of error in this estimation problem,
we consider the spatial oversampling provided by the Quickbird data to be well suited to address the
fundamental question in the mixing problem. The validity of using high resolution vegetation
fractions to validate moderate resolution fractions therefore depends on whether there is a consistent
bias in the linear mixing model that corrupts both the moderate and high resolution estimates in
such a way that they are mutually consistent but consistently wrong.
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Convolution and resampling of the 2.6 meter vegetation fractions at 30 meter resolution makes it
possible to assess the geographic coregistration and to compare the moderate resolution estimates
and the high resolution measurements directly. Comparison of the Quickbird image to the handheld
GPS measurements showed a generally ENE displacement of 10 to 30 meters. As this is within the
spatial uncertainty of GPS receiver and the expected geolocation error of both images, we did not
attempt to relocate either image. Visual comparison of the interactively overlaid 30 meter images
showed no evidence for systematic misregistration. A density shaded scatterplot of the 30 meter
ETM+ estimates versus the 30 meter resampled Quickbird vegetation fractions is shown in Figure
2. The linear correlation coefficient for the 80850 (245x330) coregistered 30 meter pixels is 0.89.
Medians and interquartile ranges calculated at 1% increments indicate that the ETM+ estimates
agree with the Quickbird vegetation fractions to within 5% for fractions greater than 0.2 and that
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50% of ETM+ fractions agree to within 10%. The ETM+ fractions are consistently higher than the
Quickbird estimates for fractions less than 0.2 with the positive bias diminishing monotonically
approaching 0.2. Scatter about the 1:1 line increases for fractions up to ~0.3 and diminishes for
higher fractions. We investigate two possible causes for this scatter by simulating the effects of
spatial misregistration and systematic estimation error.
The scatter about the 1:1 line could result from 1) error in the ETM+ fraction estimates or from 2)
subpixel (< 30 m) spatial misregistration between the ETM+ and Quickbird images or from 3) a
combination of estimate error and spatial misregistration. Spatial misregistration of the images
causes the spatial correlation to diminish as the scatter increases with offset. The effect of spatial
misregistration can be simulated by introducing a series of geographic offsets to identical 2.8 meter
vegetation fraction images, convolving each image with the ETM+ spatial response function,
resampling each to 30 meter resolution and comparing the correlation of the displaced 30 meter
images.
We simulate the combined effects of spatial misregistration and estimation error by comparing
scatterplots of perturbed versus unperturbed vegetation fractions. By varying the amount of
misregistration and the amount of estimation error we can compare the dispersion of the resulting
scatterplots with that observed in Figure 2. The effect of geolocation error combined with
estimation error by adding specified amounts of normally distributed random noise to each pixel in
the perturbed image. The distribution of scatter is most similar to that seen for a northeastward
misregistration of 17 meters with less than 3% estimation error or an 11 meter misregistration with
less than 6% estimation error.
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